From quantum to classical via crystallization

We show that classical states can emerge as pure ground state solutions of a quantum many-body system. We use a simple Hubbard model in 1D with strong short-range interactions and a second nearest neighbor hopping with N particles arranged among M sites. We show that the ground state of this Hubbard chain for M=2N-1 consists of a single many-body state where the strongly interacting particles arrange in a classical state with crystalline order. The ground state is separated by an energy gap from the first excited state, and survives in the thermodynamic limit for large N. The energy gap increases linearly with the strength of the interaction between the particles making the classical ground state robust to external perturbations like disorder. Our result is an example of how a quantum system can converge to a classical state, like a crystal, without requiring decoherence, wavefunction collapse or other external mechanisms.